Question: Solve for $x$ and $y$ using elimination. ${-3x+5y = -2}$ ${-3x+2y = -8}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${3x-5y = 2}$ $-3x+2y = -8$ Add the top and bottom equations together. $-3y = -6$ $\dfrac{-3y}{{-3}} = \dfrac{-6}{{-3}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-3x+5y = -2}\thinspace$ to find $x$ ${-3x + 5}{(2)}{= -2}$ $-3x+10 = -2$ $-3x+10{-10} = -2{-10}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {-3x+2y = -8}\thinspace$ and get the same answer for $x$ : ${-3x + 2}{(2)}{= -8}$ ${x = 4}$